Characteristics of an Adjustable Speed Polyphase Induction Machine

Variable frequency stepped-voltage wav eforms generated by an SCR bridge-inverter are used to drive a 3-phase induction motor. The system coefficient matrix associated with the volt- ampere differential equations of a polyphase induction machine is cyclic symmetric about its major diagonal axis. A basic property of this type of matrix is that it can be diagonalized by a transformation of variables by use of the well-known symmetrical component transformation. Here mutual cross-coupling terms give rise to speed- sensitive coefficients in the solution equations. Hence, the contribution presented in this paper is in the formulation of the solution of high-order complex systems in closed form. Solutions are obtained for phase currents and line and phase voltages on a per mode basis, where a mode is defined as one sixth of a cycle. Two cases arise as a result of both speed and slip conditions of the load. In one case conduction takes place over each entire mode and in the other case conduction ceases at some intermode time τ
_p
. The latter case requires two sets of solution equations per mode. Torque equations are derived and typical response curves are plotted. Experimental testing of a prototype system corroborates derived analytical solutions.